Abstract Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional-order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.
Shi Peng(石鹏) , Cao Guo-Wei(曹国威), and Li Yong-Ping(李永平) Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform 2010 Chin. Phys. B 19 074201
[1]
Siegman A E 1986 Lasers (California: Mill Valley) p35
[2]
Ariz'on V and Ojeda-Castaneda J 1995 Opt. Lett. 20 118
[3]
Modregger P, Lübbert D, Sch?fer P, K?hler R, Weitkamp T, Hanke M and Baumbach T 2008 Opt. Express 16 5141
[4]
Rodrigo J A, Cheben P, Alieva T, Calvo M L, Florjanczyk M, Janz S, Scott A, Solheim B, Xu D X and Del'age A 2007 Opt. Express 15 14631
[5]
Muffoletto Richard P, Tyler J M and Tohline J E 2007 Opt. Express 15 5631
[6]
Onural Levent 2007 J. Opt. Soc. Am. A 24 359
[7]
Kopp C and Meyrueis P 1998 Opt. Commun. 158 7
[8]
Deng X, Bihari B, Gan J, Zhao F and Chen R 2000 J. Opt. Soc. Am. A 17 766
[9]
Pellat-Finet P, Durand P and Fogret 'E 2006 Opt. Lett. 31 3429
[10]
Liu Z J and Liu S T 2007 Opt. Lett. 32 2088
[11]
Zheng C W 2006 Phys. Lett. A 355 156
[12]
Deng X, Li Y, Fan D and Qiu Y 1997 Opt. Commun. 138 270
[13]
Pei S C and Yeh M H 1997 Opt. Lett. 22 1047
[14]
Zhou G Q 2009 Chin. Phys. 18 2779
[15]
Xu G L, Wang X T and Xu X G 2010 Chin. Phys. B 19 014203
[15]
Yuan L 2008 Chin. Phys. B 17 170
[16]
Gao Q, Liao T H and Cui Y F 2008 Chin. Phys. B 17 2018
[17]
Tucker S B, Ojeda-Castaneda J and Cathey W T 1999 J. Opt. Soc. Am. A 16 316
[18]
Shi P, Liu Q, Cao G W and Li Y P 2009 Acta Phys. Sin. 58 5392 (in Chinese)
[19]
Marinho F J and Bernardo L 1998 J. Opt. Soc. Am. A 15 2111
[20]
Bastiaans M J 1978 Opt. Commun. 25 26
[21]
Bastiaans M J 1979 J. Opt. Soc. Am. A 69 1710
[22]
Oh Se Baek and Barbastathis George 2009 Opt. Lett. 34 2584
[23]
Pan Wei Qing 2008 Appl. Opt. 47 45
[24]
Wu P, Lu B D and Chen T L 2005 Chin. Phys. 14 1009
[25]
Lohmann A W 1993 J. Opt. Soc. Am. A 10 1130
[26]
Mas David, Garcia Javier, Ferreira Carlos, Bernardo Luis M and Marinho Francisco 1999 Opt. Commun. 164 233 endfootnotesize
Decoherence of elliptical states in phase space Wang Yue-Yuan (王月媛), Liu Zheng-Jun (刘正君), Liao Qing-Hong (廖庆洪), Wang Ji-Cheng (王继成), Liu Shu-Tian (刘树田). Chin. Phys. B, 2011, 20(5): 054201.
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